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Gal, Mahamadi Warma","submitted_at":"2015-09-10T12:50:11Z","abstract_excerpt":"We consider a degenerate parabolic equation associated with the fractional $% p $-Laplace operator $\\left( -\\Delta \\right) _{p}^{s}$\\ ($p\\geq 2$, $s\\in \\left( 0,1\\right) $) and a monotone perturbation growing like $\\left\\vert s\\right\\vert ^{q-2}s,$ $q>p$ and with bad sign at infinity as $\\left\\vert s\\right\\vert \\rightarrow \\infty $. We show the existence of locally-defined strong solutions to the problem with any initial condition $u_{0}\\in L^{r}(\\Omega )$ where $r\\geq 2$ satisfies $r>N(q-p)/sp$. 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Gal, Mahamadi Warma","submitted_at":"2015-09-10T12:50:11Z","abstract_excerpt":"We consider a degenerate parabolic equation associated with the fractional $% p $-Laplace operator $\\left( -\\Delta \\right) _{p}^{s}$\\ ($p\\geq 2$, $s\\in \\left( 0,1\\right) $) and a monotone perturbation growing like $\\left\\vert s\\right\\vert ^{q-2}s,$ $q>p$ and with bad sign at infinity as $\\left\\vert s\\right\\vert \\rightarrow \\infty $. We show the existence of locally-defined strong solutions to the problem with any initial condition $u_{0}\\in L^{r}(\\Omega )$ where $r\\geq 2$ satisfies $r>N(q-p)/sp$. 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